# Understanding the Confidence Interval

The confidence interval is a central concept of hypothesis testing. Although understanding its mathematical and statistical meaning is beyond the scope of this module, one needs to have a fair idea of the concept. Hence, a brief introduction of the confidence interval that is essential for the Six Sigma project team to understand is as follows:

### Point Estimates v/s Interval Estimates

The normal distribution is a continuous distribution. This means that the probability of reaching the exact point is zero. This conclusion has profound implication for estimation. This is because instead of reaching a point estimate, one needs to pen down an interval estimate to get a realistic answer. Thus we can’t say the probability of the value being exactly 100. However, we can make a fairly educated guess about whether the value will lie between 80 and 120.

### What is Confidence Interval ?

A confidence interval attaches a probability to the above statement. For instance if we say that a value will lie between 80 and 120 with 90% confidence, we mean to say that there is a 9 out of 10 chance that this will be the case. However statistics operate on the law of large numbers and hence these values are expected to hold true only after a large number of experiments have been performed.

The confidence interval is therefore a result of using sampling. In the above case we can conclude that in a sample 90% of the total observations taken will have the value lying between 80 and 120.

### What Factors Influence the Confidence Interval ?

The factors that influence the confidence interval have been listed down along with their precise relationship:

• Sample Size: The confidence level increases as the sample size increases. This is because as the sample size grows, there is more evidence. The sample is in fact closer to the population and hence the more the data, the less the chances of sampling error.

• Sample Variation: Obviously the confidence interval would get larger as the sample variation decreases. If the samples are homogenous, you can be more confident about the predictions that you make

### Relationship to Hypothesis Testing

Hypothesis testing is almost always done on samples. Hence, we must understand that there can be a difference between the values drawn from the samples and the actual value of the population. This is what we call sampling error. This plays a vital role in interpretation of hypothesis testing. Hypothesis tests with a higher confidence level are more accurate than the ones with lower confidence levels.

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Six Sigma - Analyze Phase